| 1. | \(\left[M^2LT^{-2}A^{-2}\right]\) | 2. | \(\left[MLT^{-2}A^{2}\right]\) |
| 3. | \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\) | 4. | \(\left[ML^{2}T^{-2}A^{-2}\right]\) |
Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\), the mutual inductance \(M\) between them will be directly proportional to:
| 1. | \(\dfrac{R_1}{R_2}\) | 2. | \(\dfrac{R_2}{R_1}\) |
| 3. | \(\dfrac{R^2_1}{R_2}\) | 4. | \(\dfrac{R^2_2}{R_1}\) |
A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)